In order to solve Problem  for any given value
of the time discretization parameter \(N\) , we shall over-approximate
reachable sets \(\mathcal {R}(t_i)\)  and
reachable tubes \(\mathcal {R}( {t_i, t_{i+1}} )\) 
of the control system REF  for equidistant points of
time \(t_i \in {t_0, t_f}\) , \(i \in {0;N}\) .
The approximation will be convergent of first order
[1]},
meaning that
the Hausdorff distance between \(\mathcal {R}(t_i)\)  and its
approximation is of order \(O(1/N)\) , and similarly for
tubes.
The respective method of over-approximation,
presented in Section REF ,
applies to any uncertainty sets \(X_0\)  and \(U\)  satisfying Hypothesis
REF  and assumes the ability to
compute with compact convex sets in finite dimension.
Our algorithmic solution subsequently presented in Section
REF  applies to the case of zonotopic
uncertainties, uses only linear algebraic operations, and
involves an additional approximation step that yields
zonotopic over-approximations of reachable tubes
retaining first order accuracy.
